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Lottery vs. Lightning: Shock and Odds

Date: 01/09/2011 at 02:10:40
From: Mark 
Subject: odds of being hit by lightning 4 times and surviving 

My name is Mark. I am a 4-time lightning strike survivor from North
Carolina.

What are the odds someone will be hit by lightning four times and survive?

Also ... with that in mind ... for the sake of comparison (since friends
ask me): what are the odds I could win the lottery?

All these electrical shocks have affected my math skills, and I would like
someone else to figure this out so I can share it with friends :) 



Date: 01/11/2011 at 18:58:19
From: Doctor Wallace
Subject: Re: odds of being hit by lightning 4 times and surviving 

Dear Mark,

Most people who survive a lightning strike describe it as a traumatic
experience. Congratulations to you on living through it ... four times!

So many variables are involved with where lightning will strike that there
isn't any theoretical way to compute that part of it. We just have to
infer the probability by using statistics. (We'll also have to use
averages, since I don't have any better data. Someone who works around
electrical equipment, for example, or in an area where thunderstorms are
common, is going to have a higher chance of being struck by lightning than
the average person is.)

According to the National Lightning Safety Institute:

   Average number of
    lightning strike 
    victims per year:       1,000

       US Population 
   as of 2000 census: 280,000,000

So they arrive at a 1/280,000 probability of being struck in any given
year.

From there, we can calculate the probability of it happening four times by
multiplying the individual probabilities:

     (1/280,000) * (1/280,000) * (1/280,000) * (1/280,000)
   =  1/6.14 x 10^21

Let's try to put this into perspective, and address your second question
along the way.

Your home state of North Carolina participates in the Powerball lottery.
The probability of winning the jackpot (assuming a 59/39 game, which is
usual) is roughly 1 in 195 million.

This means that you are about 696 times more likely to get struck by
lightning once than you are to win Powerball. (One hundred ninety-five
million divided by 280,000 is about 696.)

But struck FOUR times?

If we divide the earlier result by 195 million, we get:

          6.14 x 10^21
        ---------------  = 3.15 x 10^13
          1.95 x 10^8

This means your chance of winning Powerball is a whopping 31.5 TRILLION
times greater than being struck by lightning four times.

Wow.

You are one unlucky guy for being struck four times -- and one lucky guy
for surviving!

Thanks for writing to Dr. Math.

Don't hesitate to write again if you need further help with this or
another question.

- Doctor Wallace, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
Middle School Probability

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